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I am using finite element software to solve ODEs and PDEs. It requires the semilinear form. E.g When solving the poisson equation $$\nabla\cdot((1+u^2)\nabla u) = -f$$ the semilinear form $$\int_\Omega (1+u^2)\nabla u\cdot\nabla v - fvdx$$ is required.

What I would like to know is the semilinear form for the equation $$\nabla^2 u = -f(u)$$

DJames
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1 Answers1

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Assuming that $\nabla^2u$ is the Laplacian, it would most likely be

$$\int_\Omega\nabla u\cdot\nabla v + f(u)v.$$

Essentially it should be the nonlinear form that defines the weak formulation?

Ellya
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